Fastest Distributed Consensus Problem on Fusion of Two Star Sensor Networks

Finding optimal weights for the problem of fastest distributed consensus on sensor networks with different topologies has been an active area of research for a number of years. In this work, we present an analytical solution for the problem of Fastest Distributed Consensus for a sensor network formed by fusing two different symmetric star sensor networks. In other words, a sensor network consisting of two different symmetric star sensor networks which are sharing the same central node. The solution procedure consists of stratification of associated connectivity graph of network and Semidefinite Programming (SDP), particularly solving the slackness conditions. The optimal weights are obtained by inductive comparing of the characteristic polynomials initiated by slackness conditions. Some numerical simulations are carried out to investigate the tradeoff between the parameters of two fused star sensor networks, namely, the length and number of branches. Also, the obtained optimal weights has been compared with different weighting methods by evaluating the Second Largest Eigenvalue Modulus (SLEM) and comparing convergence time improvements numerically. Moreover, several examples of two fused star sensor networks with branches other than path graphs are introduced along with their optimal weights and SLEM.